Respuesta :
You probably looking to write the given expression as a single logarithm.
Remember the follwing rules:
log(ab)= log(a) + log(b)
log(a/b)=log(a) - log(b)
log(a)^b = b log(a)
Based on these rules, we can write the above expression as a single logarithm, as shown below:
[tex]log(9)+ \frac{1}{2}log(x)+log( x^{3}+4)-log(6) \\ \\ =log(9)+ log(x)^{ \frac{1}{2} } +log( x^{3}+4)-log(6) \\ \\ =log( \frac{9 \sqrt{x}( x^{3}+4) }{6} ) \\ \\ =log( \frac{3 \sqrt{x}( x^{3}+4) }{2} )[/tex]
Remember the follwing rules:
log(ab)= log(a) + log(b)
log(a/b)=log(a) - log(b)
log(a)^b = b log(a)
Based on these rules, we can write the above expression as a single logarithm, as shown below:
[tex]log(9)+ \frac{1}{2}log(x)+log( x^{3}+4)-log(6) \\ \\ =log(9)+ log(x)^{ \frac{1}{2} } +log( x^{3}+4)-log(6) \\ \\ =log( \frac{9 \sqrt{x}( x^{3}+4) }{6} ) \\ \\ =log( \frac{3 \sqrt{x}( x^{3}+4) }{2} )[/tex]
